Are there any helicopters with ejection seats? If so, how is the clearance problem with the rotating blades solved?
As others above have stated, the Kamov KA-50 family is fitted with an ejection seat. First the blades are separated from the blade sleeves, which remain attached to the mast (rotor hub). a few fractions of a second later, the conventional upwards firing ejection seat is launched, using extraction rockets tied to cables to drag the seat clear of the airframe.
This cutaway image shows it to reasonable effect. '46' indicates where the blade separates from the sleeve. The little sketch of the smoke on the lower right blade shows the separation, and the '18' and '19' show the extraction rocket. KA-50 Cutaway image
Many years ago I read about the Kamov-50 helicopter family* being the first helicopters equipped with ejection seats. And Wikipedia verifies my memory:
It is the world's first operational helicopter with a rescue ejection system, which allows the pilot to escape at all altitudes and speeds.
In the same article for the same helicopter it is mentioned that
Before the rocket in the ejection seat deploys, the rotor blades are blown away by explosive charges in the rotor disc and the canopy is jettisoned.
As a side note, in the article I read in an aviation magazine many years ago, it mentioned a synchronization of the seat with the blade rotation so that the seat passes between the blades. It was based on a working principle similar to the middle machine gun that some WW2 German airplanes were equipped with that fired the projectiles between the propeller blades.
Judging from the fact that I read it somewhere in the late 90s where the project was still new and developing, as PlasmaHH pointed out, that was probably more a thought rather than a fact.
* Kamov 50 and its variants/successors like Ka52
The Sikorsky S-72 Rotor Systems Research Aircraft had ejection seats, as shown on this video. Like the Ka-50, it blew the rotor blades off first before ejecting.
This article mentions a crash of a Mi-28 in which one pilot died:
The Mi-28 was supposedly designed with an ejection seat system that fires its crew out the side and downward.
The Mi-28 doesn't actually have the ejection seats, the Mikoyan constructor bureau follows a different approach: they've created energy absorbing seats and landing gear to protect the pilot in a crash.
Kamov does install ejection seats in their helicopters, a.o. in the Ка-52. It blows off the rotor blades and shatters the upper glass windows to make the way clear for pilot ejection. One can see the white cord with explosive on the upper window of Ka-52 on the pictures (there is a white zigzag-like cord on the bottom of the pilot window):
Testing of the part of the system